Global convergence analysis of a class of epidemic models

Abstract

• Global convergence of an endemic equilibrium (EE) of the epidemic models. • Global asymptotic stability of a disease free equilibrium (DFE). • Does not rely on traditional Lyapunov functions. • Simplified and innovative stability analysis of an endemic equilibrium (EE). This paper addresses the global convergence of the epidemic models whose infected subsystems are monotone in the sense of Hirsch (1984). By invoking results from monotone system theory and nonlinear control theory, a simple method is proposed for determining the global asymptotic stability of a disease free equilibrium (DFE) and the global convergence to an endemic equilibrium (EE). Typical epidemic models are studied to illustrate the applicability of the proposed methodology.